limit___lxz的博客

不定型00\frac{0}{0}00​方法：等价无穷小洛必达法则麦克劳林公式习惯u(x)v(x)  ⟹  ev(x)lnu(x)u(x)^{v(x)} \implies \quad e^{v(x)lnu(x)}u(x)v(x)⟹ev(x)lnu(x)ln(...)  ⟹  (联想)ln(1+Δ)ln(...) \implies(联想)\quad ln(1+\Delta)ln(...)⟹(联想)ln(1+Δ)(...)−1  ⟹  (...) - 1 \implies(...)−1⟹

0<a1<π，an+1=sinan0 \lt a_1 \lt \pi，a_n+_1=sina_n0<a1​<π，an​+1​=sinan​，求证lim⁡n→∞an ∃\lim_{n \to \infty} a_n\space\existslimn→∞​an​ ∃，并求出证：∵0<a1<π0 \lt a_1 \lt \pi0<a1​<π，∴a2∈(0,1)⊂(0,π2)a_2\in(0,1)\subset(0,\frac{\pi}{2})